# Department of Mathematics Syllabus

This syllabus is advisory only. For details on a particular instructor's syllabus (including books), consult the instructor's course page. For a list of what courses are being taught each quarter, refer to the Courses page.

MAT 21M: Accelerated Calculus

**Approved:**, Brian Osserman

**ATTENTION:**

This course is part of the inclusive access program, in which your textbook and other course resources will be made available online. Please consult your instructor on the FIRST DAY of instruction.

**Units/Lecture:**

5

**Suggested Textbook:**(actual textbook varies by instructor; check your instructor)

Thomas' Calculus Early Transcendentals, 14th Edition by George B. Thomas, Maurice Weir, and Joel Hass; Addison Wesley Publishers.

Search by ISBN on Amazon: 978-0321884077

Search by ISBN on Amazon: 978-0321884077

**Prerequisites:**

5 on AP exam, Must stasify the Mathematics Placement Requirement

**Suggested Schedule:**

Limits:

- Precise definition (2.3)
- Limit laws (2.2)
- One-sided limits (2.4)
- Continuity (2.5)
- Infinite limits & asymptotes (2.6)

~ 5 lectures

Derivatives:

- Tangents & derivative at a point (3.1)
- The derivative as a function (3.2)
- Differentiation rules (3.3)
- Derivative as a rate of change (3.4)
- Derivatives of trig functions (3.5)
- Chain rule (3.6)
- Implicit differentiation (3.7)
- Derivative of inverse functions and logarithms (3.8)
- Inverse trig functions (3.9)
- Related rates (3.10)
- Linearization and differentials (3.11)

~ 5.5 lectures

Applications of derivatives:

- Extreme values (4.1)
- The Mean Value Theorem (4.2)
- Monotone functions and first derivative test (4.3)
- Concavity and curve sketching (4.4)
- Indeterminate forms and l'Hopital's Rule (4.5)
- Applied optimization (4.6)
- Newton's method

~ 4.5 lectures

Integrals:

- Antiderivatives (4.8)
- Estimation with finite sums (5.1)
- Limits of sums (5.2)
- Definite integrals (5.3)
- Fundamental Theorem of Calculus (5.4)
- Substitution (5.5-5.6)

~ 3.5 lectures

Applications of integrals:

- Volumes of solids of revolution (6.1-6.2)
- Arc length (6.3)
- Surface area (6.4)
- Work (6.5)
- Moments and centers of mass (6.6, 1-dimensional only)

~ 3 lectures

Transcendental functions:

- Logarithm as an integral (7.1)
- Separable different equations (7.2)

~ 1.5 lectures

Integration Techniques:

- Parts (8.2)
- Trigonometric (8.3)
- Trig substitution (8.4)
- Partial fractions (8.4-8.5)
- Numerical integration (8.7)
- Improper Integrals (8.8)

~ 4 lectures

Parametrization and polar coordinates:

- Parametric Curves (11.1-11.2)
- Polar coordinates (11.3-11.4)

-- To be covered in discussion sections

Total of 27 lectures, leaving 3 lectures for in-class exams, introductory discussion and/or schedule adjustments.

**Additional Notes:**

Two weekly discussion sections. Students are expected to know a great deal of AP-level calculus coming in, and this is tested by a
preliminary exam early in the quarter. Lectures emphasize material not typically absorbed well in high school.